Results 161 to 170 of about 1,525 (197)

Semisimple Lie Groups

2012
In the preceding chapter, we studied groups with a compact Lie algebra. For these groups, we have seen how to split them into a direct product of a compact and a vector group, how to complement the commutator group by an abelian Lie group, and that all compact Lie groups are linear.
Joachim Hilgert, Karl-Hermann Neeb
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Semisimple subgroups of linear semisimple Lie groups

Journal of Mathematical Physics, 1975
The problem of embedding a semisimple Lie group in a linear semisimple Lie group [where one (or both) may be noncompact] is investigated in detail. The analysis is based on a previous set of papers dealing with the corresponding problem for real Lie algebras.
Cornwell, J. F., Ekins, J. M.
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On the centre of a transitive semisimple lie group

Annals of Global Analysis and Geometry, 1988
The paper deals with the study of the connected semisimple Lie groups acting transitively and effectively on a simply connected compact homogeneous manifold or a noncompact homogeneous manifold with two ends. The author establishes several results about the order and the rank of such a Lie group G.
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Representations of Noncompact Semisimple Lie Groups

Journal of Mathematical Physics, 1970
A method is presented for the construction of unitary representations of semisimple Lie groups (or, more precisely, of the corresponding algebras), proceeding directly from the commutation relations among the canonical generators e±α and hα. In the case of the orthogonal groups, the correspondence between the canonical generators and the more usual ...
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Complex Semisimple Lie Groups

1990
This chapter deals with the most explored section of the theory of Lie groups and Lie algebras. Its main result is the complete classification of connected complex semisimple Lie groups and their irreducible linear representations. This classification is based on the theory of root systems, which because of its numerous applications deserves a special ...
Arkadij L. Onishchik, Ernest B. Vinberg
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Real Semisimple Lie Groups

1990
Our study of real semisimple Lie groups and algebras is based on the theory of complex semisimple Lie groups developed in Ch. 4. This is possible because the complexification of a real semisimple Lie algebra is also semisimple (see 1.4.7). However, the correspondence between real and complex semisimple Lie algebras established with the help of the ...
Arkadij L. Onishchik, Ernest B. Vinberg
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Groups generating transversals to semisimple lie group actions

Israel Journal of Mathematics, 1991
The orbit structure of finite measure preserving actions of non-compact Lie groups exhibits a wide range of very strong rigidity properties. The main theorem of the paper describes those countable groups with finite measure preserving actions that are stably orbit equivalent to such an action of a higher rank simple Lie group. This is applied to obtain
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Exceptional Unitary Representations Of Semisimple Lie Groups

Representation Theory, 1996
Let G G be a noncompact simple Lie group with finite center, let
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Structure of Semisimple Lie Groups

1980
Chapter I presents a brief resume, with occasional indications of proofs, of the theory of semisimple Lie groups up to (but not including) Cartan’s highest weight theory for finite-dimensional representations and the theory of parabolic subgroups. We start with some basic notions of linear algebra (Section 1) and do the representations of sl(2) which ...
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On the Isomorphism and Diffeomorphism of Compact Semisimple Lie Groups

Mathematical Notes, 2022
V V Gorbatsevich, Gorbatsevich V V
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